Microparticle Hydrogel Material Properties Emerge from Mixing-Induced Homogenization in a Poly(ethylene glycol) and Dextran Aqueous Two-Phase System

Polymer–polymer aqueous two-phase systems (ATPSs) are attractive for microgel synthesis, but given the complexity of phase separation, predicting microgel material properties from ATPS formulations is not trivial. The objective of this study was to determine how the phase diagram of a poly(ethylene glycol) (PEG) and dextran ATPS is related to the material properties of PEG microgel products. PEG-dextran ATPSs were prepared from four-arm 20 kDa PEG-norbornene and 40 kDa dextran in phosphate buffered saline (PBS), and the phase diagram was constructed. PEG microgels were synthesized from five ATPS formulations using an oligopeptide cross-linker and thiol-norbornene photochemistry. Thermogravimetric analysis (TGA) revealed that the polymer concentration of microgel pellets linearly correlates with the average concentration of PEG in the ATPS rather than the separated phase compositions, as determined from the phase diagram. Atomic force microscopy (AFM) and bulk rheology studies demonstrated that the mechanical properties of microgels rely on both the average concentration of PEG in the ATPS and the ATPS volume ratio as determined from the phase diagram. These findings suggest that PEG-dextran ATPSs undergo homogenization upon mixing, which principally determines the material properties of the microgels upon gelation.


Figure S1
: Representative 1 H NMR spectrum of PEG-amide-norbornene.The peaks that correspond to alkene protons in norbornene from 5.91-6.31ppm were normalized to the peak that correspond to protons in the PEG backbone from 3.57-3.84ppm, which was 454 H for one arm of the polymer.Based on these integrations, functionalization was calculated to be 91%.

Determination of Tie Lines
Tie-lines were calculated from the following system of mass balance equations.Where m denotes total mass in mg, and X, Y, and Z denote concentrations in wt% of PEG, dextran, and PBS, respectively.In all variables, the subscripts mix, top, and bot refer the variable to the total mixture, the top phase, and the bottom phase, respectively.
(Equation S1) Moreover, the fit for the binodal has previously been determined, and is described by the function, f(x) (Equation 1).The binodal relates the concentration of dextran in either separated phase to the concentration of PEG in that same phase.Thus, plugging in concentrations of dextran into Equation 1 provides two more equations, as shown below, giving a system of seven equations total.
(Equation S6)   = (  ) (Equation S7) The five known variables in the system of equations are m mix , m top , X mix , Y mix , and Z mix .The seven unknown variables are m bot , X top , Y top , Z top , X bot , Y bot , Z bot .The number of unique equations equals the number of unknown variables, so a unique solution exists.The system of equations was solved for each ATPS formulation and tie-lines were constructed from the compositions of the separated phases.Tie-lines for the microgel formulations were interpolated from the empirically determined tie-lines by arc-length continuation of the conjugate curve.

Figure S2 :
Figure S2: Relationship between ATPS composition and the polymer concentration of packed microgel pellets.The TGA data presented in Figure 5.A was related to the average PEG concentration in the ATPS and the dextran:PEG volume ratio (Equation 02).Adj R2 and Pred R2 are the adjusted and predicted coefficients of determination respectively.Please see Mov S1 for a 3D representation of the model surface.Data point color corresponds to microgel formulation as follows: Red: Soft, Blue: Intermediate 1, Green: Intermediate 2, Purple: Intermediate 3, Yellow: Stiff.

Figure S3 :
Figure S3: Relationship between ATPS composition and the micromechanical stiffnesses of individual microgels.The AFM data presented in Figure 6.A was linearly related to the average PEG concentration in the ATPS.Adj R2 and Pred R2 are the adjusted and predicted coefficients of determination respectively.Data point color corresponds to microgel formulation as follows: Red: Soft, Blue: Intermediate 1, Green: Intermediate 2, Purple: Intermediate 3, Yellow: Stiff.Average values and standard deviations for each microgel formulation may be found in Figure 6A.

Figure S5 :
Figure S5: Microgel scaffolds were subjected to shear strain sweeps.The averages of at least three strain sweeps per microgel scaffold formulation were calculated and are plotted above.Error bars are standard deviations.Square markers refer to storage modulus and triangle markers refer to loss modulus.Data marker colors correspond to microgel scaffold formulations as follows: Red: Soft, Blue: Intermediate 1, Green: Intermediate 2, Purple: Intermediate 3, Yellow: Stiff.